A new norm-relaxed method of strongly sub-feasible direction for inequality constrained optimization

Combining the norm-relaxed method of feasible direction (MFD) with the idea of strongly sub-feasible direction method, we present a new convergent algorithm with arbitrary initial point for inequality constrained optimization. At each iteration, the new algorithm solves one direction finding subproblem (DFS) which always possesses a solution. Some good properties of the new algorithm are that it can unify automatically the operations of initialization (Phase I) and optimization (Phase II) and the number of the functions satisfying the inequality constrains is nondecreasing, particularly, a feasible direction of descent can be obtained by solving DFS whenever the iteration point gets into the feasible set. Under some mild assumptions without the linear independence, the global and strong convergence of the algorithm can be obtained.